Answer:
0 days: 4
1 day: 4
2 days: 5
3 days: 6
4 days: 6
5 days: 7
10 days: 10
15 days: 15
20 days: 33
25 days: 51
30 days: 79
Step-by-step explanation:
Answer: x = 8
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I'm going to use the notation log(2,x) to indicate "log base 2 of x". The first number is the base while the second is the expression inside the log (aka the argument of the log)
log(2,x) + log(2,(x-6)) = 4
log(2,x*(x-6)) = 4
x*(x-6) = 2^4
x*(x-6) = 16
x^2-6x = 16
x^2-6x-16 = 0
(x-8)(x+2) = 0
x-8 = 0 or x+2 = 0
x = 8 or x = -2
Recall that the domain of log(x) is x > 0. So x = -2 is not allowed. The same applies to log(2,x) as well.
Only x = 8 is a proper solution.
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You can use the change of base rule to check your work
log base 2 of x = log(2,x) = log(x)/log(2)
log(2,(x-6)) = log(x-6)/log(2)
So,
(log(x)/log(2)) + (log(x-6)/log(2)) = 4
(log(8)/log(2)) + (log(8-6)/log(2)) = 4
(log(8)/log(2)) + (log(2)/log(2)) = 4
(log(2^3)/log(2)) + (log(2)/log(2)) = 4
(3*log(2)/log(2)) + (log(2)/log(2)) = 4
3+1 = 4
4 = 4
The answer is confirmed
Answer:
B: y = -2/3x - 10/3
Step-by-step explanation:
The point is at (-2,-2), therefore when you input -2 into the desired equation, it should yield -2 as our output. If we use the equation B, the equation becomes
-4/3 - 10/3 which is -6/3. After dividing it we get -2 as the output.
To find the line yourself we use the point slope formula
y - y1 = m(x - x1)
The line is parallel to the one on the graph so the slope or <em>m</em> is equal to -2/3
We input the coordinates we want for y1 and x1.
y - (-2) = -2/3 (x - (-2))
y + 2 = -2/3x - 4/3
y + 6/3 = -2/3x - 4/3
y = -2/3x - 10/3
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